4x^2 -49 4x^2 -1
---------------- ÷ ---------------------------
14x^2 + 53x+14 14x^2 -3x -2
copy dot flip
4x^2 -49 1 4x^2 -3x-2
---------------- * ---------------------------
14x^2 + 53x+14 4x^2 -1
factor each term
(2x-7) (2x+7) (7 x + 2) (2 x - 1)
------------------- * ---------------------------
(7 x + 2) (2 x + 7) (2x-1)(2x+1)
Cancel
(2x-7) (7 x + 2)
------------------- * ---------------------------
(7 x + 2) (2x+1)
(2x-7) (7 x + 2)
----------------------------
(7 x + 2) (2x+1)
Continue to cancel
(2x-7)
----------------------------
(2x+1)